Studies of Fragment Angular Distributions in the Fission ofBi209andU238Induced by Alpha Particles of Energies up to 115 MeV

Using semiconductor detectors, the fragment angular distributions have been measured in the cases of fission of ${\mathrm{Bi}}^{209}$ and ${\mathrm{U}}^{238}$ induced by alpha particles of various energies ranging from 23 to 115 MeV obtained from the Berkeley 88-in. variable-energy cyclotron. The center-of-mass angular distributions were analyzed by a least-squares fitting code to obtain the value of ${K_0}^2$ corresponding to the saddle-point excitation energy ${E_x}^s$ for each bombarding energy. The transmission coefficients $T_l$ and the mean square of the orbital angular momentum $〈l^2〉$ of the fissioning nucleus required for deducing ${K_0}^2$ were determined from optical-model calculations. For both the cases of compound nuclei of ${\mathrm{At}}^{213}$ and ${\mathrm{Pu}}^{242}$, it is found that the values of ${K_0}^2$ increase more rapidly with ${E_x}^s$ than expected on the basis of the Fermi-gas model, irrespective of the assumptions made about the multiple-chance fissions. The fission cross sections of ${\mathrm{U}}^{238}$ for alpha-particle energies up to 110 MeV, also measured in this work, enabled us to check the accuracy of the optical-model calculations. The presence of direct interactions and their effects on the deduced values of ${K_0}^2$ were also investigated in detail in the case of the target nucleus ${\mathrm{U}}^{238}$. Using the standard expression for $\frac{{\Gamma }_n}{{\Gamma }_f}$, the first-chance values of ${K_0}^2$ have been obtained and further corrected for the estimated direct-interaction effects, in the case of the target nucleus ${\mathrm{U}}^{238}$. Even after allowance is made for the direct-interaction effects, the energy dependence of ${K_0}^2$ appears to be significantly different from that expected on the basis of the simple Fermi-gas model. These results can be explained within the framework of the Fermi-gas model if it is assumed that $\frac{J_{\mathrm{eff}}}{{a_f}^{\frac{1}{2}}}$ increases significantly with the bombarding energy. It appears likely that these results suggest a rapid increase in the effective moment of inertia $J_{\mathrm{eff}}$ with the angular momentum, as can be expected on the basis of the observed steep variation in the saddle shapes with $\frac{Z^2}{A}$.